A sheet processing apparatus such as a mail sorting machine includes a stacking unit as a paper sheet stacking apparatus which stacks sheets sorted into a plurality of sorting destinations. The stacking unit includes a plurality of stackers associated with the plurality of sorting destinations, respectively, and a conveyance mechanism which conveys sheets into each stacker. The stacking unit conveys each sheet received from the main body of the sheet processing apparatus into a stacker corresponding to the sorting destination of this sheet. However, the stacking unit of the conventional sheet processing apparatus cannot detect any skew that occurs during conveyance in the stacking unit. In the conventional sheet processing apparatus, problems may occur in a process of stacking sheets in the stackers due to a skew that occurs during conveyance in the stacking unit.